Lagrangian perspectives on advection-diffusion transport in the low-diffusivity limit

Daniel Karrasch (TU München)

Jan 23. 2020, 15:30 — 16:00

We study transport of weakly diffusive passive tracers in Lagrangian coordinates and in the low-diffusivity limit. In Lagrangian coordinates, the associated advection-diffusion equation is of time-inhomogeneous diffusion equation type, even for time-homogeneous diffusion in the Eulerian frame. Our main results are of averaging type: over finite-time intervals the time-inhomogeneous diffusion equation is approximated by the time-averaged (time-homogeneous) diffusion equation in two ways. The generator of the time-averaged diffusion/heat semigroup is a Laplace operator (Froyland’s dynamic Laplacian) associated to a weighted manifold structure on the material manifold. This dynamically induced manifold structure has been introduced earlier by Karrasch & Keller and coined geometry of mixing. We establish relationships between surface area in the geometry of mixing and diffusive transport through material surfaces. This is joint work with Nathanael Schilling (TUM).

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Mathematical Aspects of Geophysical Flows (Workshop)
Organizer(s):
Adrian Constantin (U of Vienna)
George Haller (ETH Zurich)